Shelvey has six England caps to his name, but the last of those came in November 2015, and he was not involved in the international friendlies against the Netherlands and Italy last month.
Cottee has claimed that the national team will need something different against the likes of Tunisia and Panama, and has called on Gareth Southgate to call up the former Liverpool midfielder.
"Whether you're talking about Eric Dier, Jake Livermore, Jack Wilshere or Jordan Henderson, whoever you name that's been in that England squad, there isn't anyone who can pass the ball better than Shelvey," Cottee told Sky Sports News.
"He needs to keep doing it for the last five or six games, but if he carries on like he is, he deserves to have a chance of getting on that plane. When we're playing the likes of Tunisia and Panama, we're going to have a lot of the ball. You need someone who can do something different.
"You need a Wilshere in the team, or a Shelvey, who can open up defences. You don't want loads of workmanlike midfielders who don't create and pass the ball. Jonjo brings something different to the table. I wouldn't definitely have him in the squad, but if I was Gareth Southgate I'd be looking at him and thinking very carefully.
"He's probably the best English passer, in terms of passing it 40-50 yards. That's not smashing the ball forward, that's quality passing. What you need to do with him is get some legs around him in the team, if he's going to spread the ball around, but I think he would give the squad something different."
Shelvey has scored twice in 27 appearances for Newcastle this season.